Presently, data communications devices ("DCDs") and other data communications equipment ("DCE"), such as analog and digital modems, terminal adapters and routers, for example, are used to transfer or transport data between data terminal equipment ("DTE") such as personal computers, workstations, mainframe computers, and other terminals, over various communications channels such as telephone lines, T1 or ISDN lines, which also may be part of a computer network. Typically, the data is transmitted, received, or otherwise transferred in the form of a digitally encoded communication signal, which may include, for example, digitally encoded data transmitted on a carrier signal, having a predetermined or otherwise specified center frequency, that is modulated by a predetermined constellation (or transmit constellation) of signal points (such as quadrature amplitude modulation), at a particular (and usually predetermined) signaling rate. In current and proposed systems, the signaling constellation may include from five hundred to over 1600 signaling points.
At the sending or transmitting DCE, a carrier signal is thus modulated with the set of constellation signal points corresponding to the digital code or value to be transported over the channel. The channel, however, typically introduces or allows a variety of impairments or noise which affect the transmitted signal, such as amplitude distortion, envelope delay distortion, non-linear distortion, additive noise, white noise, and other distortions. For example, the transmission channel may introduce an impairment which shifts or displaces the frequency of the carrier, referred to herein as "carrier frequency offset", which may result in impaired or erroneous demodulation. With carrier frequency offset, a signal transmitted at a frequency of, for example, 1800 Hz, may actually be received from the channel or network at a frequency of 1801 Hz. In addition, the sending DCE signaling rate may not exactly match the receiving DCE signaling rate, affecting the sampling rate and sampling timing and, as a consequence, affecting the determination of the amplitude and phase of the received signal. This difference between the sending DCE signaling rate and the receiving DCE signaling rate will be referred to herein as "timing frequency offset". For example, the sending DCE may have a timing reference of 2401 Hz, the receiving DCE may have a timing reference of 2399 Hz, when both should have a timing reference of 2400 Hz. Before the digital data can be transported, therefore, the receiving DCE should both synchronize to the sending DCE signaling rate and also remove or accommodate the carrier frequency offset caused by the channel.
In order for the receiving DCE to both synchronize to the sending DCE signaling rate and also remove or accommodate the carrier frequency offset caused by the channel, prior art methods and apparatus have essentially incorporated the use of phase locked loops to track the carrier and timing frequency offsets. Other prior art methods and apparatus have incorporated the use of algorithms to track error, such that an initially large estimated error may converge over a period of time to a more accurate assessment of actual error. Other prior art methods have used band-edge timing compensation averaging using either some (and usually not all) of the available tones (of the training sequence) or a wide-band signal.
A significant difficulty with such prior art methods and apparatus is often the length of time needed for them to properly and accurately determine and account for the carrier and timing frequency offsets. Typically, upon system start-up, as discussed in more detail below, each of the connected modems transmits a probe signal and other information to the other connected modem, engaging in a training period. The duration of the training period for determining and responding to the various parameters of the probe signal, however, may be relatively short. While the various iterative, phase locked loop and other methods mentioned above may ultimately provide reasonably accurate or usable results if given enough time and repetitions, such time may be unavailable or undesirable for high speed data transmission. As a result, there continues to be a need to provide data communications equipment with a mechanism for both rapidly and accurately determining and responding to both the timing frequency offset and the carrier frequency offset given a received probe signal, with a training period which has a limited duration.